Lauren Cranton Heller

e-mail: lch@math.berkeley.edu
office: Evans 775

Department of Mathematics
University of California, Berkeley
970 Evans Hall
Berkeley, CA 94720



MATH 32

LEC 001: Evans 10, MWF 3-4

office hours: M 11:30-12:30, F 2-3, or by appointment

a short survey for the first day of class, and an evaluation for the middle of the semester

course information

We will use the third edition of Precalculus: A Prelude to Calculus by Sheldon Axler.

Homework will be due (in person) at the beginning of discussion on the days listed in the schedule below. Late homework will not be accepted. Quizzes will occur during discussion and will cover the textbook sections indicated in the schedule below. Problems will be similar to those on the homework.

If you cannot attend my office hours, please give me a list of times when you are free so we can schedule a meeting.

More information is included in the syllabus. You can also use this form to send me a question or comment anonymously. (Berkeley login required.)

Visit the SLC for information about the adjunct course, tutoring, and other services.

discussion

GSI office hours discussion sections
Nafisa Arain Evans 858 DIS 101: Evans 4, MW 8-9
Tu 4-5, Th 12:30-1:30 DIS 102: Latimer 121, MW 9-10
Scott Mutchnik Evans 832 DIS 103: Latimer 122, MW 9-10
F 11-1 DIS 105: Evans 4, MW 10-11
Emily Bain Evans 1049 DIS 104: Evans 2, MW 10-11
Tu 12-2 DIS 106: Latimer 121, MW 11-12
Madeline Brandt Evans 1065 DIS 107: Dwinelle 79, MW 11-12
F 10-12 DIS 108: Dwinelle 79, MW 12-1
Theresa Honein Evans 858 DIS 109: Evans 5, MW 1-2
M 12-1, W 2-3 DIS 110: Dwinelle 130, MW 8-9

homework

hw 1 0.2: 6-52 evens; 53,55 scan
0.3: 2-28 evens; 75-79 all scan
hw 2 0.3: 32-36,42-46,58-62 evens; 64-65,69-71 all sol 0
1.1: 2-26,34-46 evens; 62,68
hw 3 1.2: 6-28 evens; 51-53 all
1.3: 4-60 multiples of 4; 71
1.4: 2-14,22-26,40-46 evens; 65-66 all
hw 4 1.5: 2-24,34 evens; 39,43-44 all
1.6: 2-14 evens; 39-41,44 all sol 1
2.1: 4,10-16,26-36,42-44 evens; 47,57-58 all
hw 5 2.2: 14-24,36-40 evens; 48-60,76-80 multiples of 4; 99
2.4: 4-28 multiples of 4; 33,35,43,49-50 all
2.5: 2-12,28-32,36-42 evens; 47
hw 6 2.3: 4-20,28-56,80-100 multiples of 4; 120-122 all sol 2
3.1: 8-36,56-76 multiples of 4; 85,90-92 all
hw 7 3.2: 4-8,46-48 evens; 50,52-54,56 all
3.3: 12-34 evens; 59-67 all
hw 8 3.5: 8-22,38-50 evens
3.7: 2-16,26-28 evens; 36 sol 3
4.2: 2-24,32,36-38,42-46 evens; 51
hw 9 4.3: 2-6,12-24 evens; 35-38 all
4.4: 8-20 evens; 24-40 multiples of 4; 43-45
4.5: 2-4,10-30 evens; 43 rev 4
hw 10 5.1: 2-10,18-20,26-30,36,42-48 evens; 55-56 all
4.6: 8-72 multiples of 4; 74,88,90 all
hw 11 5.2: 4-12,20-28,36-40 multiples of 4; 43-50 all
5.4: 4-8,12-24 evens; 26,28,30-32 all
5.5: 12-56,64-68 multiples of 4; 74
hw 12 5.6: 6-36 evens
5.7: 2-32 evens

exams

exam 1 (solutions)

exam 2 (solutions)

schedule

8/28 0.2algebra
8/30 0.3absolute values
9/2 NO CLASS
9/4 0.3inequalities hw 1 due
9/6 1.1functions
9/9 1.2graphs quiz 0.2-0.3
9/11 1.3transformations hw 2 due
9/13 1.4composition
9/16 1.5inverses quiz 0.3-1.2
9/18 1.6more graphs hw 3 due
9/20 2.1lines
9/23 2.2conics quiz 1.3-1.5
9/25 2.4polynomials hw 4 due
9/27 2.5rational functions
9/30 extra time quiz 1.6-2.2
10/2 review
10/4 EXAM
10/7 2.3exponents
10/9 CLASS CANCELED
10/11 CLASS CANCELED
10/143.1logarithms quiz 2.4-2.5, hw 5 due
10/163.2power rule hw 6 due
10/183.3product and quotient rules
10/213.5e and ln quiz 2.3,3.1
10/233.7exponential growth hw 7 due
10/254.2radians
10/28 CLASS CANCELED
10/304.3cosine and sine quiz 3.2-3.3,3.5, hw 8 due
4.4tangent, etc. [remote lecture]
11/1 4.5right triangles
11/4 5.1inverse trig. functions quiz 3.7,4.2-4.3
11/6 review
11/8 EXAM
11/11 NO CLASS
11/134.6identities hw 9 due
11/155.2more identities
11/185.4laws of sines and cosines quiz 4.5-4.6,5.1
11/205.5double- and half-angle formulas hw 10 due
11/225.6addition and subtraction formulas
11/255.7more transformations hw 11 due
11/27 NO CLASS
11/29 NO CLASS
12/2 extra time quiz 5.4-5.6
12/4 extra time hw 12 due
12/6 review
12/17 FINAL 7-10 pm (location TBD)



qualifying exam

commutative algebra / algebraic geometry

Consider the rings k[s^2,st] and k[s^2,t^2]. What are their dimensions? Are they integrally closed? How do they relate to maps to projective space?

How about k[s^3,s^2t,st^2,t^3]?

Calculate a Grobner basis for for the ideal (xz,yw,xw) in k[x,y,z,w].

Give the Koszul complex on the generators of this ideal. Is it a resolution?

Define the canonical curve of genus 4 and describe its ideal sheaf.

Find the Picard group of a nonsingular quadric.

Draw a picture of Spec Z[x].

differential geometry

What are the maximal ideals in the ring of smooth functions on a compact manifold?

Define the tangent space.

Given a vector field X, do there exist local coordinates under which X is constant?